Ppt on Quantum Computing

QQUANTUM UANTUM CCOMPUTINGOMPUTING

PRESENTED BY:PRESENTED BY:

Lakshmi Devi JindalLakshmi Devi Jindal

www.studygalaxy.com

CONTENTSCONTENTS

IntroductionIntroduction

History of Quantum ComputingHistory of Quantum Computing

Quantum Computer BasicsQuantum Computer Basics

Implementation of Quantum ComputingImplementation of Quantum Computing

Applications of Quantum ComputingApplications of Quantum Computing

Current progressCurrent progress

ConclusionConclusion

INTRODUCTIONINTRODUCTION

A A Quantum ComputerQuantum Computer is a computer that is a computer that harnesses the power of atoms and harnesses the power of atoms and molecules to perform memory and molecules to perform memory and processing tasks. It has the potential to processing tasks. It has the potential to perform certain calculations billions of perform certain calculations billions of times faster than any silicon-based times faster than any silicon-based computer.computer.

QUANTUM COMPUTER BASICSQUANTUM COMPUTER BASICS

In the classical model of a computer, the most In the classical model of a computer, the most fundamental building block, the bit, can only exist in one fundamental building block, the bit, can only exist in one of two distinct states, a 0 or a 1. In a quantum computer of two distinct states, a 0 or a 1. In a quantum computer the rules are changed the rules are changed

qubit qubit exist in the classical 0 , 1 state and coherent exist in the classical 0 , 1 state and coherent superposition of both. superposition of both.

Two UniversesTwo Universes

Increasing the number of qubits therefore exponentially Increasing the number of qubits therefore exponentially increases the 'quantum parallelism' we can obtain with increases the 'quantum parallelism' we can obtain with the system. the system.

……CONTINUEDCONTINUED

A quantum computer is nothing like a classical A quantum computer is nothing like a classical computer in design; you can't for instance build computer in design; you can't for instance build one from transistors and diodes. In order to build one from transistors and diodes. In order to build one, a new type of technology is needed, a one, a new type of technology is needed, a technology that enables 'qubits' to exist as technology that enables 'qubits' to exist as coherent superpositions of 0 and 1 states. The coherent superpositions of 0 and 1 states. The best method of achieving this goal is still best method of achieving this goal is still unknown, but many methods are being unknown, but many methods are being experimented with and are proving to have experimented with and are proving to have varying degrees of success.varying degrees of success.

IMPLEMENTATION OF IMPLEMENTATION OF QUANTUM COMPUTINGQUANTUM COMPUTING

Quantum DotsQuantum Dots

Computing liquidsComputing liquids

An implementation of the qubit is the 'quantum An implementation of the qubit is the 'quantum dot' which is basically a single electron trapped dot' which is basically a single electron trapped inside a cage of atoms. When the dot is exposed inside a cage of atoms. When the dot is exposed to a pulse of laser light of precisely the right to a pulse of laser light of precisely the right wavelength and duration, the electron is raised wavelength and duration, the electron is raised to an excited state: a second burst of laser light to an excited state: a second burst of laser light causes the electron to fall back to its ground causes the electron to fall back to its ground state. The ground and excited states of the state. The ground and excited states of the electron can be thought of as the 0 and 1 states electron can be thought of as the 0 and 1 states of the qubit and the application of the laser light of the qubit and the application of the laser light can be regarded as a controlled NOT function as can be regarded as a controlled NOT function as it knocks the qubit from 0 to 1 or from ' to 0.it knocks the qubit from 0 to 1 or from ' to 0.

QUANTUM DOTSQUANTUM DOTS

PROBLEMSPROBLEMS

Unfortunately there are a number of practical problems Unfortunately there are a number of practical problems that are preventing this from happening:that are preventing this from happening:

The electron only remains in its excited state for about a The electron only remains in its excited state for about a microsecond before it falls to the ground state. Bearing microsecond before it falls to the ground state. Bearing in mind that the required duration of each laser pulse is in mind that the required duration of each laser pulse is around 1 nanosecond, there is a limit to the number of around 1 nanosecond, there is a limit to the number of computational steps that can be made before information computational steps that can be made before information is lost. is lost. Constructing quantum dots is a very difficult process Constructing quantum dots is a very difficult process because they are so small. A typical quantum dot because they are so small. A typical quantum dot measures just 10 atoms (1 nanometer) across. The measures just 10 atoms (1 nanometer) across. The technology needed to build a computer from these dots technology needed to build a computer from these dots doesn't yet exist. doesn't yet exist.

COMPUTING LIQUIDSCOMPUTING LIQUIDS

The latest development in quantum computing takes a The latest development in quantum computing takes a radical new approach. It drops the assumption that the radical new approach. It drops the assumption that the quantum medium has to be tiny and isolated from its quantum medium has to be tiny and isolated from its surroundings and instead uses a sea of molecules to surroundings and instead uses a sea of molecules to store the information. When held in a magnetic field, store the information. When held in a magnetic field, each nucleus within a molecule spins in a certain each nucleus within a molecule spins in a certain direction, which can be used to describe its state; direction, which can be used to describe its state; spinning upwards can signify a 1 and spinning down, a spinning upwards can signify a 1 and spinning down, a 0.0.


Spinning of atoms can Spinning of atoms can represent bitsrepresent bits– Spinning down Spinning down

represents 0represents 0– Spinning up represents 1Spinning up represents 1– Spinning both ways is Spinning both ways is

called a “super-position”called a “super-position”

These bits is called These bits is called “qubits”“qubits”


The quantum computer in this technique is the molecule The quantum computer in this technique is the molecule itself and its qubits are the nuclei within the molecule. itself and its qubits are the nuclei within the molecule. This technique does not however use a single molecule This technique does not however use a single molecule to perform the computations; it instead uses a whole to perform the computations; it instead uses a whole 'mug' of liquid molecules. 'mug' of liquid molecules.

The advantage of this is that even though the molecules The advantage of this is that even though the molecules of the liquid bump into one another, the spin states of the of the liquid bump into one another, the spin states of the nuclei within each molecule remain unchanged. nuclei within each molecule remain unchanged. Decoherence is still a problem, but the time before the Decoherence is still a problem, but the time before the decoherence sets in is much longer than in any other decoherence sets in is much longer than in any other technique so far. technique so far.

APPLICATIONAPPLICATION

Shor’s Algorithm:Shor’s Algorithm:

This is an algorithm invented by Peter Shor in This is an algorithm invented by Peter Shor in 1995 that can be used to quickly factories large 1995 that can be used to quickly factories large numbers. If it is ever implemented it will have a numbers. If it is ever implemented it will have a profound effect on cryptography, as it would profound effect on cryptography, as it would compromise the security provided by public key compromise the security provided by public key encryption (such as RSA). encryption (such as RSA).

STAGE ISTAGE I

The first stage of the algorithm is The first stage of the algorithm is to place a memory register into a to place a memory register into a coherent superposition of all its coherent superposition of all its possible states. The letter 'Q' will possible states. The letter 'Q' will be used denote a qubit that is in be used denote a qubit that is in the coherent state. A calculation the coherent state. A calculation performed on the register can be performed on the register can be thought of as a whole group of thought of as a whole group of calculations performed in calculations performed in parallel, one in each universe. In parallel, one in each universe. In effect, a calculation performed effect, a calculation performed on the register is a calculation on the register is a calculation performed on every possible performed on every possible value that register can value that register can represent.represent.

STAGE IISTAGE II

The second stage of the algorithm performs a calculation The second stage of the algorithm performs a calculation using the register. The details of which are as follows: using the register. The details of which are as follows:

The number The number NN is the number we wish to factorise, is the number we wish to factorise, NN = 15 = 15 A random number A random number XX is chosen, where 1 < is chosen, where 1 < XX < < NN-1 -1 XX is raised to the power contained in the register (register is raised to the power contained in the register (register A) and then divided by A) and then divided by NN The remainder from this operation is placed in a second 4 The remainder from this operation is placed in a second 4 bit register (register B). bit register (register B).


After this operation After this operation has been has been performed, register performed, register B contains the B contains the superposition of superposition of each universes each universes results. results.


Notice that the contents of register B Notice that the contents of register B follows a repeating sequence follows a repeating sequence (1,2,4,8,1,2,4,8...), the frequency at which (1,2,4,8,1,2,4,8...), the frequency at which this repeats can be named this repeats can be named ff. In this case . In this case the repeating sequence (1, 2, 4, 8) has the repeating sequence (1, 2, 4, 8) has four values so four values so ff = 4. = 4.

STAGE IIISTAGE III

The frequency of repetition, The frequency of repetition, ff, can be , can be found. This is done by performing a found. This is done by performing a complex operation on register B and then complex operation on register B and then looking at its contents which causes the looking at its contents which causes the results from every universe to interfere results from every universe to interfere with each other. with each other.

CAN THE RESULT BE CAN THE RESULT BE GUARANTEED?GUARANTEED?

The resulting number cannot be guaranteed to be a The resulting number cannot be guaranteed to be a prime factor, but there is a good chance that it is one. prime factor, but there is a good chance that it is one. The interference that produces the value for The interference that produces the value for ff tends to tends to favour the correct answer as incorrect answers cancel favour the correct answer as incorrect answers cancel each other out.each other out.In our example the value In our example the value ff = 4 does give a correct = 4 does give a correct answer of 3.answer of 3.The fact that the answer cannot be guaranteed to be The fact that the answer cannot be guaranteed to be correct is of little consequence as it can be easily correct is of little consequence as it can be easily checked with multiplication. If the answer is incorrect, checked with multiplication. If the answer is incorrect, there is a very strong chance that repeating the there is a very strong chance that repeating the calculation a few times with different values of calculation a few times with different values of XX will will produce the right answer.produce the right answer.

CURRENT PROGRESSCURRENT PROGRESS

The recent work on the 'computing liquid' technique pioneered by The recent work on the 'computing liquid' technique pioneered by Dr. Gershenfield and Dr. Chuang (Los Alamos National Laboratory, Dr. Gershenfield and Dr. Chuang (Los Alamos National Laboratory, New Mexico) has given quantum computing a promising future. In New Mexico) has given quantum computing a promising future. In fact, Dr. Gershenfield believes that a quantum co-processor could fact, Dr. Gershenfield believes that a quantum co-processor could be a reality within 10 years if the current pace of advancement be a reality within 10 years if the current pace of advancement continues. Other techniques, such as quantum dots, may also yield continues. Other techniques, such as quantum dots, may also yield similar results as our technology advances. The optimist will point similar results as our technology advances. The optimist will point out that the problems being experienced by researchers appear to out that the problems being experienced by researchers appear to be technical rather than fundamental.be technical rather than fundamental.

On the other side of the argument, is the topic of decoherence. This On the other side of the argument, is the topic of decoherence. This problem has not been resolved and many people, including Rolf problem has not been resolved and many people, including Rolf Landauer of IBM's Thomas Watson Research Centre, believe that Landauer of IBM's Thomas Watson Research Centre, believe that the quantum computer is unlikely to progress beyond the 10-qubit the quantum computer is unlikely to progress beyond the 10-qubit system (described above), as decoherence makes them too fragile system (described above), as decoherence makes them too fragile to be practical.to be practical.

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